A vector is a mathematical object that represents both magnitude (size) and direction in space. It is typically represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.
u+w refers to the vector sum of two vectors u and w, which is the result of combining the magnitudes and directions of the two vectors. On the other hand, mag(u)+mag(w) refers to the sum of the magnitudes of the two vectors. In other words, u+w takes into account both magnitude and direction, while mag(u)+mag(w) only considers magnitude.
U+w is greater than mag(u)+mag(w) when the two vectors are not in the same direction. In other words, if the two vectors are pointing in different directions, the vector sum will be greater than the sum of the magnitudes.
Yes, if the two vectors are in the same direction, then u+w will be equal to mag(u)+mag(w). This is because the vector sum will be in the same direction as the individual vectors, resulting in a larger magnitude.
To add two vectors, you can use the head-to-tail method or the parallelogram method. In the head-to-tail method, you place the tail of one vector at the head of the other vector, and the resulting vector will be drawn from the tail of the first vector to the head of the second vector. In the parallelogram method, you draw the two vectors from a common point, and the resulting vector is the diagonal of the parallelogram formed by the two vectors.